On the Kohn--Sham density response in a localized basis set

We construct the Kohn–Sham density response function ${\chi }_0$ in a previously described basis of the space of orbital products. The calculational complexity of our construction is $O(N^2{N}_{\omega })$ for a molecule of $N$ atoms and in a spectroscopic window of $N_{\omega }$ frequency points. As a first application, we use ${\chi }_0$ to calculate molecular spectra from the Petersilka–Gossmann–Gross equation. With ${\chi }_0$ as input, we obtain correct spectra with an extra computational effort that grows also as $O(N^2 N_{\omega})$and,therefore,lesssteeplyin$N$thanthe$O(N^{3})$ complexity of solving Casida’s equations. Our construction should be useful for the study of excitons in molecular physics and in related areas where ${\chi }_0$ is a crucial ingredient.